Numbers or Numerals? A) C)

220 120 - 100 + 120 120 1010 ✔ ✔

B) D)

100 102 - 20 + 102 11 211 ✔ ?

Given that A, B and C are correct is D correct or incorrect?

My Dyscalculia

2

Dyscalculia I have Dyslexia and Dyscalculia (and a few other

neurological differences), they run in my family,

inherited principally from my maternal grandfather but

exhibited in different ways by various family members.

I also have a number of strengths in some areas -

these also differ between family members.

Fortunately as I am able to use these I have

succeeded in successful study to post graduate level

and worked in education, including teaching IT and

special needs teaching. 3

Factors From my own experience and from working with children and

adults who have 'failed' educationally I would say that there are a

number of interconnected factors which come in to play in

dyscalculia, as in dyslexia.

These include:

• core deficits, core strengths,

• short term or working memory issues,

• long term memory problems

• and the emotional effects - caused by teachers, peers and

family.

4

Stigma

Dyslexia has become fairly socially acceptable and literary

correctness has declined in social importance as we

approach a 'post literate' society so that it doesn't

automatically link to a stigma implying lack of intelligence

however even in this age of calculators and spreadsheets

poor levels of numeracy still do.

People are very ready to jeer at others who have no idea

what the answer to '8x12' is just because they do. Most

people have forgotten learning multiplication tables and

imagine that they are a mental prowess.

5

Paternoster I think that there is a timing element to my (and others') neuro-cognitive

difficulties which interferes with both learning and recall as well as

calculating.

If you have ever played with those toys where marbles or ball bearings are

moved by a bucket system, or if you have used the Paternoster lift in the

Arts Tower you may understand what I mean. If the flow (marbles or

people) is not regulated to the speed of the process, in this case the lift

system, it will not function efficiently.

Some mental processes take too long and overflow the holding capacity of

something I will call working memory, because of a failure in rote learning

- supply speed and or working memory - carrying capacity.

This is why the problem is worse under situations of pressure.

6

Numeric ability is not unified

Peoples' dyscalculia varies, just as their dyslexia does.

Numeric ability, just like textual ability is not a unified thing

- it just seems that way to people who have no areas of

deficit.

I have observed variations in people I have worked with but I

can most clearly tell you how my dyscalculia is manifested

and impacts at studying at undergraduate and post graduate

level.

7

My Dyscalculia

• Inability to learn number patterns by rote such as times table

• Problems with left / right orientation / reading direction -

especially with decimals

• Difficulty maintaining in mind the arithmetic rule in use

• Difficulty remembering place in a number string so poor at

transcribing long numbers

• Limited 'space' in short term memory - not able to remember

number sequences

8

• Limited time for short term memory - if task cannot be

completed quickly it just evaporates, especially when there

are distractions - that is in a typical class room setting

• Difficulty reading numbers and symbols, that is, being slow at

working out what is written with confusable items such as 3,

Σ, 5, S, & and 8 or '.' and ',' - among others.

• Difficulty reading numbers in small boxes or when too widely

spaced or irregularly spaced, mixed with words, not justified

etc.

9

• Inability to do anything in more than one modality, as for

instance when a different thing is presented visually from what

a lecturer is saying

• Inability to write numbers down when dictated

• Emotional issue of fearing looking stupid or being told I am by

teachers or lecturers for not getting the answer in the way or

time that they demand

• As above for getting the answer right by a non conventional

means and being accused of cheating

10

Overlap I think that you will see from the above list that it can be difficult to

function in a typical lecture situation without experiencing a good deal of

stress.

Some problems of dyscalculia are related to the dyslexia or shared with

it, others are distinct deficits.

This is possibly why up to 50% of people with dyslexia have dyscalculia

- one or more core number failures plus dyslexia - which compounds

the problems experienced in a typical academic setting.

Given that around a third of people with dyscalculia have dyslexia that

leaves a large number of students with potentially unidentified

dyscalculia.

11

'I have never taught a student

with dyscalculia' I studied advanced statistics at masters level at another university.

Even though I explained my difficulty to the lecturers most of the teaching

sessions provoked every area of difficulty listed, (except for the last one). In

addition variable names used were short (and to me meaningless,

indistinguishable) abbreviations.

I could not keep up during sessions because I couldn't find things or work

them out quickly enough.

Information was given in speech, not writing, with unnumbered PowerPoint

slides flicked between computer screens displays and shifting up and down.

I had no way to find where I was to make notes about the slides or refer to

my own computer. 12

I tried to prepare for sessions by reading up and working through the

material in advance. This failed as the two principal lecturers didn't

believe in following the time table.

There was a third lecturer who clearly knew his material well and

wanted to share his enthusiasm.

He asked questions to check that people understood him - not to show

them up or check that they were listening.

He had clearly prepared written materials and worked through PPTs in

order, following the hand out and the timetable, presenting one idea at

a time in a logical progression.

If teaching styles are bad for students with dyslexia and Dyscalculia

they are probably not good for the rest of the students. 13

Arithmetic is not Mathematics

Finally I would like to point out that most issues with dyscalculia, for

the majority, seem to relate to arithmetic, especially mental arithmetic

and when under stress, time constraint and distraction. There are

people with dyscalculia who become advanced mathematicians. As

arithmetic is presented as maths many who fail never progress with

the subject long enough to gain a level of mathematical understanding.

They have been so emotionally beaten down.

I believe that dyscalculia per se is not the problem. The problem is the

high value placed on rote learning in arithmetic teaching combined

with the stigma attached to failure to learn number facts and patterns,

which is reinforce by teachers' disparaging remarks.

14

I never pay attention to anything by

"experts" People who do not have 'typical' minds are more likely to

develop unique thinking.

I like the quote from Richard Feynman about fallibility -

'I never pay attention to anything by "experts". I

calculate everything myself.'

He stressed that rote learning was a poor approach to

teaching maths because studying function is more valuable

than form.

15

References

Feynman, R.P. (1985). Feynman, Surely You're

Joking, Mr. Feynman. WW Norton & Company, New

York.

Feynman, R.P. (1965). New textbooks for the" new"

mathematics. Engineering and Science 28: 9-15.

16